1. Field of the Invention
The present invention relates to instruction means for teaching arithmetical operations and, more particularly to a teaching device for the instruction of pupils in the long division and long multiplication of numbers and optionally other arithmetical operations, such as addition, subtraction, etc.
2. Description of the Prior Art
Many devices and visual aid means are known for teaching pupils, especially precocious children, learning disabled, and other exceptional individuals, basic arithmetical operations. Generally, this is effected by means of educational toys or tutoring devices which, although exploiting the idea of visual aids, are limited to illustrative example and do not require the participation of the pupil in the learning process.
Thus, a first group of known devices is generally in the form of toys which will aid a child in learning more of a subject such as aritmetical problems and which are primarily concerned with self-teaching techniques, since only the proper answer can usually be placed in the area constructed for receiving the answer. Illustrative of such devices is U.S. Pat. No. 2,971,275 issued Feb. 14, 1951 to D. Provenzano, wherein the toy is so constructed that the fixed answer for the fixed and predetermined problem is usually structurally different from all other answers so as to combine the correct solution with the correct shape. Although these types of devices are manipulated by the pupil himself, they lack completely the ability of teaching the abstract concepts of mathematical operations.
Another aspect of teaching devices is the one directed to tutoring mathematics by means of tables which are manipulated by the student individually and are intended to test and familiarize the student with arithmetical relations. Typical of these devices is U.S. Pat. No. 2,899,756 issued Aug. 18, 1959 to P. H. Wise, in which a board has a cut-out center or recessed portion within which a plurality of cards each proportioned to fit into the recess is inserted and a plurality of numbered blocks is adapted to be placed in the recess upon a card filled therein, the cards each having indicia thereon indicating the proper order in which the cards should be placed in the recess, the indicia being in the form of arithmetical problems to which the numbers on the blocks form solutions. As clearly understandable, this type of device is a testing or examination means for strengthening the pupil's already basic knowledge of mathematics. It does not teach the necessary abstract concepts of mathematical operations but assumes that the student be already familiar with such concepts.
Still another type of educational devices, typified by U.S. Pat. No. 3,541,702 issued Nov. 24, 1970 to J. G. Cohen, utilizes book-like means or devices containing a set of transparent pages with indicia provided on like sides of each successive page, in series, so as to illustrate step by step the solution of a problem or the development of a particular system by superimposition of the pages and of the transparencies. While this system might be useful in developing the basic concept of a given operation it lacks the ability of manipulation of the teaching aid by the student and the versatility of participation by a student in modifications and changes of a problem. It is more similar to a blackboard or rather a series of blackboards than to a means for the direct learning process of a student.
Other educational devices, believed to be more closely related to my invention are typically illustrated by U.S. Pat. No. 2,936,531 issued May 17, 1960 to J. K. Pennell, Jr. and U.S. Pat. No. 3,192,650 issued July 6, 1965 to G. R. Torchia. Both of these devices, however, are directed to specific mathematical problems and therefore cannot be adapted to concepts other than those for which they are specifically devised. The former is strictly related to teaching decimal positions in long divisions; it does not extend its visual aid teaching ability to the basic concept of mathematical operations, nor is it suitable for a complete development of division operations. Similarly, the latter is directed and restricted to teaching fractions and cannot be applied to long divisions or to the development of the operation itself. Perhaps the most interesting prior art of which I am aware is U.S. Pat. No. 3,452,455 issued July 1, 1961 to T. H. Judge, wherein a board for mathematical instruction is disclosed which includes a stationary board and a movable panel, the panel having an extending part on which can be written certain numerals to be moved adjacent to other numerals on the stationary part for each in teaching the computation, particularly of division. Although this prior art attempts to depict the division process in simplified form, it does not involve the gross motor response which my invention requires in placing each numeral, or the specific symbols to be followed for each step. Furthermore, it does involve the need for writing ability thus excluding a whole age of children and entire groups of students; it is restricted by economy to particular sizes and it is limited solely to the teaching of divisions.